
The good performance of the algorithm is the result of several choices. First, the use of voxel-sets as input for our experiments instead of other shape representations such as meshes; indeed, due to the statistical properties of our large datasets, the voxel representations leads to highly stable embeddings, they are easier to generate and to maintain than surfaces, and allow to exploit the full volumetric information of the shape. Furthermore, the fact that they are regularly sampled contributes to the convergence of the Laplacian embedding towards a “geometric-aware” eigenbasis [1]}. Second, the definition of a local graph-connectivity allows the treatment of the otherwise difficult cases related to self-contacts and topology changes. These cannot be handled when completely connected graphs are defined since a self-contact would imply changes in all the pairwise distances. Furthermore, locality gives rise to very sparse Laplacian matrices and thus to an efficient calculation of the eigendecomposition (we use ARPACK). Additionally, the initialization is usually good for EM to converge in a few iterations. As a consequence, the procedure is time-efficient, and that whole matching procedure of large voxel-sets takes only a few seconds.
Finally, it is important to mention that our method can be applied to other type of data since it relies only on geometric cues and does not use the photometric information as suggested in [2]}.
